In constructing a box-and-whisker plot for the data set below, at which values would you draw the left and right sides of the box?
6, 7, 1, 3, 9, 3, 2, 5, 8, 4, 8
A. left at 3; right at 8
B. left at 2; right at 8
C. left at 2; right at 7
D. left at 3; right at 7
The answer is A. Left at 3; right at 8.
Can someone explain this question to me, I don't get it?
Well, constructing a box-and-whisker plot is a serious business, but I'm here to bring some laughter to the equation! In this case, to find the left and right sides of the box, we need to determine the lower and upper quartiles. And luckily for us, the correct answer is hilariously simple!
The left side of the box is where we draw the lower quartile, which represents the 25th percentile. And since both 3 and 4 appear in the dataset, we should draw the left side of the box at 3 or 4. Hmm, no need for a drum roll for this one!
Now, for the right side of the box, we need to draw the upper quartile, which represents the 75th percentile. And since both 7 and 8 appear in the dataset, we should draw the right side of the box at 7 or 8. Well, isn't that a barrel of laughs!
So, the correct answer is C. left at 2; right at 7. Though drawing boxes may not be the most exciting task in the world, at least we can have some fun with it! Keep up the good work!
To construct a box-and-whisker plot, you need to organize the given data in ascending order. Then, you can divide the data into quartiles.
Here are the steps to construct a box-and-whisker plot:
1. Sort the data in ascending order:
1, 2, 3, 3, 4, 5, 6, 7, 8, 8, 9
2. Find the median (Q2):
The median is the middle value of the data set. In this case, we have 11 data points, so the median is the average of the two middle values, which are 5 and 6. Thus, the median is (5 + 6) / 2 = 5.5.
3. Find Q1 (the lower quartile):
Q1 is the median of the lower half of the data set. In this case, the lower half is 1, 2, 3, 3, 4. The median of these values is 3.
4. Find Q3 (the upper quartile):
Q3 is the median of the upper half of the data set. In this case, the upper half is 6, 7, 8, 8, 9. The median of these values is 8.
5. Calculate the interquartile range (IQR):
IQR is the difference between Q3 and Q1. In this case, IQR = 8 - 3 = 5.
6. Identify outliers:
Outliers are defined as values that lie more than 1.5 times the IQR below Q1 or above Q3. However, there are no outliers in this data set.
7. Draw the box-and-whisker plot:
- The box starts at Q1 (left side of the box) and extends to Q3 (right side of the box).
- The line inside the box represents the median (Q2).
- The whiskers extend from the left and right sides of the box to the minimum and maximum values that are not outliers.
Based on the calculations and construction steps above, the answer is option C. You would draw the left side of the box at 2 and the right side of the box at 7.